By technicality, he earns 18000*5 which equals 90000, however after his investments, it is 72000.
You are rolling two dice and one coin. Find the probability of rolling a three on the first dice, a four on the second dice, and flipping a heads on the coin.
A. 1/8
B. 1/72
C. 1/112
D. 1/36
If you are rolling two dice and one coin. the probability of rolling a three on the first dice, a four on the second dice, and flipping a heads on the coin is B. 1/72.
How to find the probability?Probability of rolling a three on the first dice is 1/6, the probability of rolling a four on the second dice is 1/6, and the probability of flipping a heads on the coin is 1/2.
To find the probability of all three events happening together, we need to multiply the probabilities of each individual event:
(1/6) x (1/6) x (1/2) = 1/72
Therefore, the probability is B. 1/72.
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If f(3x) = f(3) + f(x) then show that f(1) = f(3) = f(9) = f(27) = f(81)
Answer:f(1) = f(3) = f(9) = f(27) = f(81).
Step-by-step explanation:To show that f(1) = f(3) = f(9) = f(27) = f(81), we can use the given equation and substitute x with different values.
Let x = 1:
f(3x) = f(3) + f(x)
f(3(1)) = f(3) + f(1)
f(3) = f(3) + f(1) (since f(3x) = f(3) + f(x) when x = 1)
f(1) = 0
Now, let x = 3:
f(3x) = f(3) + f(x)
f(3(3)) = f(3) + f(3)
f(9) = 2f(3)
Since we already know that f(3) = f(3) + f(1), we can substitute it into the equation above:
f(9) = 2f(3) = 2(f(3) + f(1)) = 2f(3) + 2f(1)
f(9) - 2f(3) = 2f(1)
Now let x = 9:
f(3x) = f(3) + f(x)
f(3(9)) = f(3) + f(9)
f(27) = f(3) + f(9)
We can substitute the expression for f(9) we just derived:
f(27) = f(3) + (f(9) - 2f(3))
f(27) = f(9) - f(3)
f(27) = 2f(3) - f(3)
f(27) = f(3)
Finally, let x = 27:
f(3x) = f(3) + f(x)
f(3(27)) = f(3) + f(27)
f(81) = f(3) + f(27)
We can substitute the expression for f(27) we just derived:
f(81) = f(3) + f(27)
f(81) = f(3) + f(3)
f(81) = 2f(3)
Since we know that f(27) = f(3), we can substitute it into the equation above:
f(81) = 2f(3) = 2(f(27)) = 2(f(9) - f(3)) = 2f(9) - 4f(3)
We also know that f(9) = 2f(3) + 2f(1) from our earlier work, so we can substitute it into the equation above:
f(81) = 2f(9) - 4f(3) = 2(2f(3) + 2f(1)) - 4f(3) = 4f(3) + 4f(1) - 4f(3) = 4f(1)
Therefore, we have shown that f(1) = f(3) = f(9) = f(27) = f(81).
Triangles ABD and BCD are both isosceles.
AD = BD
AC is a straight line.
Is ADC a right angle?
Clearly explain your awnswer?
Answer:I could possibly be wrong but I say no. From what I remember, with these things you can put the points wherever as long as it follows the rules you were given for each triangle.
Step-by-step explanation:
I actually drew it out, and to me it appears as it’s not, yet I could be wrong and I’m sorry if I am! Angles aren’t my best, but I’m really good at math! If you have other problems I can go over them
Molly joined an after-school bowling club. The club members go bowling once a week throughout the school year. The bowling scores are recorded for each game so that they can be analyzed at the end of each week. Which of these is a statistical question that can be answered from the data?
Option C requires the examination of the data on bowling scores to find out what Molly's mean score is, and this constitutes a statistical inquiry that can be resolved with the information that has been gathered.
The statistical question that can be answered from the data is: C) What was Molly's average bowling score?
Option A is not a statistical question because it only concerns Molly's personal feeling towards one of her bowling scores.
Option B is a factual question that does not require statistical analysis.
Option D is also a factual question that does not require statistical analysis.
However, option C involves analyzing the bowling scores data to determine Molly's average score. This is a statistical question that can be answered using the collected data.
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Complete question:
Molly joined an after-school bowling club. The club members go bowling once a week throughout the school year. The bowling scores are recorded for each game so that they can be analyzed at the end of each week. Which of these is a statistical question that can be answered from the data?
A) Which bowling score made Molly the proudest?
B) How many times did the bowling club meet?
C) What was Molly's average bowling score?
D) On what day did the bowling club begin?
Please help me desperately need help
Answer:
9) 15
10)22
11)25
Step-by-step explanation:
9)
[tex]area=\frac{bh}{2} \\30=\frac{(2x+1)4}{2} \\\\30=4x+2\\\\28=4x\\x=7\\[/tex]
substitute:
=2x+7
=2(7)+1
=15
10)
[tex]area=\frac{bh}{2} \\114=\frac{12(3x-2)}{2} \\114=18x-12\\126=18x\\7=x[/tex]
substitute:
=3x-2
=3(7)+1
=22
11)
[tex]area=h\frac{b1+b2}{2} \\\\69=\frac{4x-2}{2} \\\\69=\frac{24x-12}{2} \\\\69=12x-6\\75=12x\\x=6.25\\\\=4x\\=4(6.25)\\=25[/tex]
Given that q is indirectly proportional to r, if q=2.8 when r=11.25, what is q when r=5.25 ?
The value of q is 6
How to calculate the value of q?The constant is k
The first step the to calculate the value of the constant which is k
k= qr
Write out the parameters given in the question
The value of q is 2.8
The value of r is 11.25
k= 2.8 × 11.25
= 31.5
The value of q can be calculated by the value of k which is 31.5 and r which is 5.25
k= qr
31.5= q × 5.25
31.5= 5.25q
q= 31.5/5.25
q= 6
Hence the value q is 6
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Verify
(N+3)!÷n+ =(n+1)(n+2)(n+3)
Answer:
True
Step-by-step explanation:
A factorial means a number multiplied by all of the positive integers before it. That means both n+3! and n! have a common factor of n!. When you take out this factor of N, the fraction (n+3)!/n! ‘s denominator would be one, and the numerator would have all of the positive integers before n+3 and also being greater than n. Thus, (n+1)(n+2)(n+3)
Order the set of numbers from least to greatest.
-4.33, 4.67 , 4 1/2
Oa. 4.67, 4 -4.33
Ob. 4,-4.33, 4.67
Oc. -4.33, 4.67, 4
Od.-4.33, 4, 4.67
The tennis balls in a bag are either white or yellow. If the ratio of white balls to yellow balls is 3/10. Which of the following could not be the number of balls in the bag
The number of balls, given the ratio of white balls to yellow balls that could not be in the bag is C. 42 balls.
How to find the ratio ?The number of balls that could not be in the bag, given the ratio of white balls to yellow balls, is the number that would not give a whole number when multiplied by the ratio of white balls to yellow balls.
26 balls :
= 3 / ( 10 + 3 white balls ) x 26
= 3 / 13 x 26
= 6 balls
39 balls :
= 3 / 13 x 39
= 9 balls
42 balls :
= 3 / 13 x 42
= 9.69 balls
There therefore cannot be 42 balls.
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Options for this question include:
2639425265The fork length r (in centimeters) of a requiem shark can be approximated by r = 0.83t + 1.13, where t is the total length (in centimeters) of the shark. Find the inverse of the function.
The inverse of the function is t = (r - 1.13) / 0.83.
What is function ?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output. A function can be thought of as a rule or a machine that takes an input value and produces a corresponding output value.
The given equation is: r = 0.83t + 1.13
To find the inverse of the function, we need to solve the equation for t.
r = 0.83t + 1.13
Subtract 1.13 from both sides:
r - 1.13 = 0.83t
Divide both sides by 0.83:
(r - 1.13)/0.83 = t
So the inverse function is:
t = (r - 1.13)/0.83
Or we can write it as:
[tex]f^{(-1)(r)} = (r - 1.13)/0.83[/tex], where [tex]f^{(-1)}[/tex] represents the inverse function.
Therefore, the inverse of the function is t = (r - 1.13) / 0.83.
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Find the expected number of flips of a coin, which comes up
heads with probability 0.5,
that are necessary to obtain either h, h, h or t, t, t.
The expected value of X is given byE(X) = 1/p= 1/(1/4) = 4
To obtain either h, h, h or t, t, t, let's consider the sequence h, h, h, t, t, t. The probability of obtaining h, h, h or t, t, t is (1/2)^3 + (1/2)^3 = 1/4. Also, the probability of the first head or tail occurring on the nth flip is (1/2)^n-1. If X denotes the number of flips of a coin required to get h, h, h or t, t, t, then X has a geometric distribution with parameter p = 1/4. Hence, the expected value of X is given byE(X) = 1/p= 1/(1/4) = 4The expected number of flips of a coin, which comes up heads with probability 0.5, that are necessary to obtain either h, h, h or t, t, t is 4.
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(x+42)
3x
please help
Given:-
A right angle is given to us.It is made up of two angles (x+42)° and 3x°.To find:-
The value of " x " .Solution:-
Here the sum of the two unknown angles will be 90° as they are the angles which make up 90° . So that;
[tex]\implies x^o + 42^o + 3x^o = 90^o \\[/tex]
[tex]\implies 4x^o = 90^o - 42^o \\[/tex]
[tex]\implies 4x^o = 48^o \\[/tex]
[tex]\implies x =\dfrac{48}{4} \\[/tex]
[tex]\implies \boxed{ x = 12} \\[/tex]
Hence the value of x is 12 .
and we are done!
Part 1: "Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least $80 a week, working a combination of both jobs.
Write a system of inequalities that can be used to represent the situation. "
Part 2: Determine and state one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours.
Much appreciated!
a) The system of inequalities that can be used to represent the situation is x + y ≤ 15 and 4x + 8y ≥ 80
b) One combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours is 10 hours babysitting and 5 hours as a library assistant.
To start, we know that Edith can work no more than 15 hours per week. Therefore, we can write the following inequality:
x + y ≤ 15
Next, we know that Edith earns $4 per hour babysitting and $8 per hour as a library assistant. We want her to earn at least $80 per week, so we can write the following inequality:
4x + 8y ≥ 80
This inequality states that the total amount Edith earns from both jobs (4x + 8y) must be greater than or equal to $80.
Now that we have two inequalities, we have a system of inequalities that can be used to represent the situation:
x + y ≤ 15
4x + 8y ≥ 80
To determine one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours, we can solve this system of inequalities.
Let's solve the first inequality for y:
y ≤ 15 - x
Now we can substitute this expression for y into the second inequality:
4x + 8(15 - x) ≥ 80
Simplifying and solving for x, we get:
-4x + 120 ≥ 80
-4x ≥ -40
x ≤ 10
To find the number of hours she should work as a library assistant, we can substitute x = 10 into our expression for y:
y ≤ 15 - x
y ≤ 15 - 10
y ≤ 5
So Edith should work no more than 5 hours as a library assistant per week.
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Solve to find the value of x ? 4x -10 = 50
Answer:
x = 15
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.
Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, add 10 to both sides of the equation:
[tex]4x - 10 = 50\\4x - 10 (+10) = 50 (+10)\\4x = 50 + 10\\4x = 60[/tex]
Next, divide 4 from both sides of the equation:
[tex]4x = 60\\\frac{4x}{4} = \frac{60}{4} \\x = \frac{60}{4} = 15\\x = 15[/tex]
~
x = 15 is your answer.
~
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Answer:
[tex]\tt x=15[/tex]Step-by-step explanation:
[tex]\tt 4x -10 = 50[/tex]
Add 10 to both sides:-
[tex]\tt 4x-10+ 10 = 50+ 10[/tex][tex]\tt 4x=60[/tex]Divide both sides by 4:-
[tex]\tt \cfrac{4x}{4} =\cfrac{60}{4}[/tex][tex]\tt x=15[/tex]___________________
Hope this helps!
anyone know this , i need help again lol
Check the picture below.
A movie production company was interested in the relationship between the budget to make a movie and how well that
movie was received by the public. Information was collected on several movies and was used to obtain the regression
equation ý = 0.145x + 0.136, where x represents the budget of a movie (in millions of dollars) and y is the predicted
score of that movie (in points from 0 to 1). What is the predicted score of a movie that has a $5 million budget?
O 0.145 points
O 0.72 points
0.861 points
O 33.55 points
Answer: 0.72 pts.
Step-by-step explanation:
For the right triangles below, find the exact values of the side lengths b and d.
If necessary, write your responses in simplified radical form.
From the right triangle figure the sides are solved to be
side b = 4√2side d = 7√3 / 2How to find side b and side dThe side b and side d is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The figure describes a right triangle, and side b is calculated using sin, SOH
Sin 45 = opposite / hypotenuse
Sin 45 = b / 8
b = 8 * sin 45
b = 4√2
Solving for side d
sin 60 = d / 7
d = 7 * sin 60
d = 7√3 / 2
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r=1.94668
r=2.94668
r=3.94668
r=0.94668
The correlation coefficient for the SAT math score and the GPA of the students is given as follows:
r=0.94668.
What is a correlation?A correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It is represented by the symbol "r" and ranges from -1 to 1.
The value of the correlation coefficient indicates the strength of the linear relationship between the variables. The closer the value of "r" is to -1 or +1, the stronger the linear relationship between the variables. A value of 0 indicates that there is no linear relationship between the variables.
The correlation coefficient is calculated inserting the points of the data-set into a correlation coefficient calculator.
The points from the graph are given as follows:
(595, 3.4), (520, 3.2), (715, 3.9), (405, 2.3), (680, 3.9), (490, 2.5), (565, 3.5).
Inserting these points into a calculator, the coefficient is given as follows:
r = 0.94668.
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The school that Natalie goes to is selling tickets to a play. On the first day of ticket sales the school sold 15 adult tickets and 5 student tickets for a total of $265. The school took in $419 on the second day by selling 15 adult tickets and 16 student tickets. What is the price each of one adult ticket and one student ticket
Answer:
Let x be the price of one adult ticket, and y be the price of one student ticket.
From the information given in the problem, we can set up the following system of equations:
15x + 5y = 265 (equation 1)
15x + 16y = 419 (equation 2)
We can solve for x by subtracting equation 1 from equation 2:
15x + 16y - (15x + 5y) = 419 - 265
11y = 154
y = 14
Now we can substitute y = 14 into either equation 1 or equation 2 to solve for x. Let's use equation 1:
15x + 5(14) = 265
15x + 70 = 265
15x = 195
x = 13
Therefore, one adult ticket costs $13, and one student ticket costs $14.
Answer this question
Answer:
5/2
Step-by-step explanation:
substitute the values into the cosine rule:
(2[tex]\sqrt{7}[/tex])² = ((2x - 1)² + (2x + 1)²) - 2(2x - 1)(2x + 1)cos(60))
work out each part separately:
(2[tex]\sqrt{7}[/tex])² = 28
(2x - 1)² = 4x² - 4x + 1
(2x + 1)² = 4x² + 4x + 1
(2x - 1)² + (2x + 1)² = (4x² - 4x + 1) + (4x² + 4x + 1) = 8x² + 2
2((2x - 1)(2x + 1)cos(60)):
(2x - 1)(2x + 1) = 4x² - 1
cos(60) = √1/2 = 1/2
2(4x² - 1)(1/2) = 4x² - 1
substitute back in:
28 = (8x² + 2) - (4x² - 1)
28 = 4x² + 3
25 = 4x²
25/4 = x²
x = √(25/4)
x = 5/2
The graph of an exponential function is shown in the figure below.
The horizontal asymptote is shown as a dashed line.
Find the range and the domain
Answer:
dghcŕhĝt5dfg9yd6grdy6cjbjbknygug4ximpohyvug5h7h6g6
Make x the subject of the formula a/b = 2x/x+5
As a result, when x = -5a /, the subject of the formula a/b = 2x/(x + 5) is x. (a - 2b).
How may the subject formula for JSS3 be changed?For instance, C is the subject of the formula C = 2r, which calculates the circumference of a circle. To modify the subject of a formula is to rewrite it such that the quantities are still related in the right way. M/2 equals D if M = 2D.
In order to eliminate the fraction and make x the subject of the formula a/b = 2x/(x + 5), we can cross-multiply:
a(x + 5) = 2bx
Next, we can distribute the a:
ax + 5a = 2bx
We can now separate the x terms from the constant terms on each side:
ax - 2bx = -5a
x(a - 2b) = -5a
Finally, we can solve for x by dividing both sides by (a - 2b):
x = -5a / (a - 2b).
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Given the expression
Choose all the equivalent expressions as your answer.
b. [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex] is an equivalent expression of y√x.
d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex] is an equivalent expression of y√x.
What is an equivalent expression?Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value(s) fοr the variable(s).
Given expression y√x
a. Is not equivalent as power is rational and exponent are non equal,
b. [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex]
= [tex]\dfrac{\sqrt{x} }{\frac{1}{y}}[/tex]
= y√x
Thus, b. [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex] is an equivalent expression of y√x.
c. Is not a n equivalent expression at has a different variable.
d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex]
[tex]\rm\sqrt{ (xy^2)} }[/tex]
[tex]\rm y \sqrt{ (x)} }[/tex]
Thus, d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex] is an equivalent expression of y√x.
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5a. Evaluate \( \lim _{x \rightarrow \frac{\pi}{2}-} \tan (x) \). (Hint: Rewrite \( \tan (x) \) as \( \frac{\sin (x)}{\cos (x)} \).)
lim_{x\to{\frac{\pi}{2}}^-} \tan x is 0.
The given function can be rewritten as;$$\frac{\sin x}{\cos x}$$Let us calculate the left hand limit$$\lim_{x\to{\frac{\pi}{2}}^-} \frac{\sin x}{\cos x}=\lim_{x\to{\frac{\pi}{2}}^-} \frac{1}{\cos x}= \frac{1}{\cos \frac{\pi}{2}}=0$$Thus, the evaluation of $$\lim_{x\to{\frac{\pi}{2}}^-} \tan x$$ is 0.
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A container holds 3.5 ounces of tablets. How many grams does the container hold?
The container holds 99.223 grams of tablets.
How to convert ounces to grams?One-sixteenth of a pound is represented by the weight measurement called an ounce (oz). A slice of bread and a pencil are two items that weigh about one ounce. One fluid ounce is the same as one-eighth of a cup in terms of volume. A medication cup has a volume of roughly one liquid ounce.
To convert ounces to grams, we can use the conversion factor 1 oz = 28.3495 g.
So, the container holds:
[tex]$3.5\ \text{oz} \times 28.3495\ \frac{\text{g}}{\text{oz}} = 99.223\ \text{g}$[/tex]
Therefore, the container holds 99.223 grams of tablets.
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Can someone please help me if they cannnn :(
Step-by-step explanation:
Your debt ratio is the ratio of the credit limit you have spent.
Your debt ratio is the amount you have spent on the credit card/ the limit
You have spent $9000- $3200 = $5800
Debt ratio = 5800/9000
=58/90 = 29/45
2. Acceptable ratio is less than 43%
Is 29 out of 45 less than 43%
Convert 29/45 to percentage
29/45 /100/1 = 64.44%
You have exceeded acceptable ratio at 64.4%
Answer:
Your debt ratio is the percentage of your credit limit that you have spent.
spent $9000- $3200 = $5800
Debt to income ratio = 5800/9000 = 58/90 = 29/45
2. A satisfactory ratio is less than 43%.
Is 29 percent of 45 less than 43%?
29/45 converted to a percentage 29/45 /100/1 = 64.44%
Step-by-step explanation:
Brainliest pls
A certain test is going to be repeated until done satisfactorily. Assume that repetitions of the test are independent and that each has probability 0.25 of being satisfactory. The first 5 tests cost $100 each to perform and thereafter cost $40 each, regardless of the outcomes. Find the expected cost of running the tests until a satisfactory result is obtained.
Result obtained is $460
Answer:Let X denote the number of tests that need to be performed until a satisfactory result is obtained. Then X has a geometric distribution with p = 0.25. Therefore,X ~ Geo(0.25) E[X] = 1/p = 1/0.25 = 4 tests.For the first 5 tests, the cost is $100 each. So the cost of running the first 5 tests is 5 × $100 = $500. Thereafter, the cost of each test is $40. The expected cost of running the tests until a satisfactory result is obtained is given by:E(Cost) = $500 + E(X – 5) × $40Expected Cost = $500 + (E(X) – 5) × $40= $500 + (4 – 5) × $40= $460Therefore, the expected cost of running the tests until a satisfactory result is obtained is $460.
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PLEASE I NEED THE AWNSER IN 2 MIN
Match the situation with the correct ratio. Don't forget that you can write a ratio three ways! Also remember the different ways to find equivalent ratios (simplify, rename, table, graph, tape diagram). Make sure you pay attention to the order!! Only enter CAPITAL letters with no spaces or numbers. (Your answer should look something like this WTYUSR)
*
1. 6:15 has a ratio of 2:5
2. 10:40 has a ratio of 1:4
3. 6:28 has a ratio of 3:14 but it would be 12:56 based on the answer choices
4. 15:25 has a ratio of 3:5 but it would be 15:25 based on the answer choices
Patients arrive at a hospital emergency department according to a Poisson distribution with an average of 9 per hour. (a) What is the probability that exactly 7 patients will arrive during a 90 minutes period? (b) What is the probability that at least 30 minutes will pass until the next patient arrives? (c) If one hour has passed and no patient has arrived, what is the probability that the next patient arrives during the following 20 minutes? Problem 4: [9 points] Patients arrive at a hospital emergency department according to a Poisson distribution with an average of 9 per hour. (a) What is the probability that exactly 7 patients will arrive during a 90 minutes period? (b) What is the probability that at least 30 minutes will pass until the next patient arrives? (c) If one hour has passed and no patient has arrived, what is the probability that the next patient arrives during the following 20 minutes?
The probability that the next patient arrives during the following 20 minutes is approximately 0.776.
(a) The probability that exactly 7 patients will arrive during a 90-minute period can be found by using the Poisson distribution formula.Poisson distribution formula:P(X = x) = (e-λ * λx) / x!Where: λ is the average number of events per unit of time or space, x is the number of occurrences, e is the exponential constant equal to 2.71828.x! means x factorial that is x(x − 1)(x − 2)⋯(2)(1).Here, λ = 9/60 = 0.15 (since there are 9 arrivals in one hour, there would be 9/60 arrivals in 1 minute)We are to find the probability of exactly 7 patients arriving in 90 minutes.The time period is 90/60 = 1.5 hours. Hence, λ = 0.15 × 1.5 = 0.225P(X = 7) = (e-λ * λ7) / 7! = (e-0.225 * 0.2257) / 7! = 0.085 ≈ 0.09Therefore, the probability that exactly 7 patients will arrive during a 90 minutes period is approximately 0.09(b) We can calculate the probability of at least 30 minutes passing until the next patient arrives by using the cumulative distribution function (CDF) of the exponential distribution.Exponential distribution formula:f(x) = λe-λxwhere λ is the rate parameter, x is the time period, and e is the exponential constant equal to 2.71828.The mean waiting time between two successive arrivals is 60/9 = 6.67 minutes.Hence, λ = 1/6.67 = 0.15The probability of at least 30 minutes passing until the next patient arrives can be calculated as follows:P(X > 0.5) = 1 - P(X ≤ 0.5) = 1 - (1 - e-λx) = e-λx = e-0.15×0.5 ≈ 0.776Therefore, the probability that at least 30 minutes will pass until the next patient arrives is approximately 0.776.(c) The probability that the next patient arrives during the following 20 minutes can be calculated as follows:P(X > 1) = 1 - P(X ≤ 1) = 1 - (1 - e-λx) = e-λx = e-0.15×1/3 ≈ 0.776Therefore, the probability that the next patient arrives during the following 20 minutes is approximately 0.776.
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Find a formula for the exponential function passing through thepoints (-1, 2/5 ) and (3,250)
The exponential function between (-1, 2/5) and (3, 250) is as follows:
[tex]f(x) = 2 * 5^x[/tex]
By combining the fourth roots from both sides, we arrive at:
b = 5
When we use the expression we discovered for a and this value of b, we get:
a = (2/5) * 5 = 2
As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:
[tex]f(x) = 2 * 5^x[/tex]
what are functions?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
from the question:
This is the shape of the exponential function:
f(x) = a *[tex]b^x[/tex]
where a represents the starting point and b represents the exponential function's base.
We must solve the system of equations to determine the values of a and b that meet the requirements:
a * [tex]b^(-1)[/tex] = 2/5 (equation 1)
a *[tex]b^3[/tex]= 250 (equation 2)
We can solve for an in equation 1 by multiplying both sides by b:
a = (2/5) * b
Substituting this expression into equation 2, we get:
(2/5) * b *[tex]b^3[/tex] = 250
Simplifying, we get:
[tex]b^4 = 3125[/tex]
By combining the fourth roots from both sides, we arrive at:
b = 5
When we use the expression we discovered for a and this value of b, we get:
a = (2/5) * 5 = 2
As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:
[tex]f(x) = 2 * 5^x[/tex]
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